Graduate Student Seminar

On Ritt’s decomposition theorem

Wayne Peng, University of Rochester

Friday, April 26th, 2019
5:00 PM - 6:00 PM
Hylan 1106A

Ritt’s decomposition theorem concerns decomposition of polynomials of one indeterminant. The number of ways to decompose a polynomial is not unique and not even finite since any decomposition \(f\circ g\) can also be written as \(f\circ L\circ L^{-1}\circ g\) where \(L\) is an affine map. Nevertheless, if we define the equivalent relation between two decompositions as above, the number of complete decompositions is finite. One can show that decomposition of a polynomial, \(F=f\circ g\), is one-to-one correspondent to the intermediate fields between \(K(t)\) and \(K(F(t))\) where \(t\) is transcendental over \(K\), the defining field of \(F\) by Luroth theorem. We will also talk about the decomposition of morphism on varieties and give an example.

Event contact: junwen dot peng at rochester dot edu